GURPS takes the (realistic) approach that reaching your arm out into the reach of a swordsman is a bad idea. Basically, if someone executes a weapon parry against your sword, you just don't hit. If they execute it against your arm, well, bad things can happen to your arm.
However, in a Dungeon Fantasy game, this pretty much hoses monsters and martial artists. Realism be damned, I want my owlbears to exchange blows with swordsman and not get chopped up during their own attacks. So here are some options:
Unarmed Etiqutte from GURPS Martial Arts. Basically, armed defenses cannot be used against unarmed attacks. Like in kung fu movies and the big set-piece fight in Kill Bill vol. 1, such as right here.
Notes: This does make the fighting less gritty, though, so this isn't suited for pseudo-realistic games. It also annoys armed characters because they can only dodge monster attacks.
Half Damage Parries. The damage caused by an armed parry against an unarmed attack isn't a hard strike, it's a redirection or neutralization of the attack. So any successful parry that causes damage (per B376) rolls damage and halves it, round up.
Notes: I've used this for so many years I don't think my players realize it's not in the books. Works fine, it's believable, and makes damage on a parry a nice bonus instead of a free, extra attack.
My Hands Are Lethal Weapons. Characters with Trained By A Master cannot be harmed by a successful armed parry when attacking, and do not suffer damage when striking a high DR surface. However, you do still come in contact with the parrying weapon or the surface you strike, so you still suffer any incidental damage or problems - contact venom, spikes, burning from flaming swords, damaging auras, etc.
In a Dungeon Fantasy game or other monster-heavy game, this may apply by default to any and all monsters!
Notes: This approach makes armed characters happier, because they can still use their main defenses against unarmed/monster attacks. It also makes martial artists happy, too, because they can freely chop orc skulls and hip toss owlbears without worrying they'll be torn up every time they try. Or armor up their limbs and extremities.
Aggressive Parry (Armed). By the GURPS rules, armed parries are aggressive by default. Instead, say they aren't. If you parry normally, you can't hurt the unarmed attacker. If you parry aggressively, at -1 (unless you buy it up), you can attempt an armed aggressive parry using the normal rules in GURPS Martial Arts, p. 65, with the modifiers listed for swing or thrust equally.
Notes: Gives a tradeoff - possible free damage to the attacker, but at a cost of possibly whiffing your defense. Unarmed fighters still have to worry about getting hurt, though.
Too Fast For Your Sword. There are a few options here. One is to allow the Rapid Retraction perk to give its bonus as a penalty to the roll to injure on a parry. Another is an Average Technique or Leveled Perk, up to 3 or 4 levels, which gives a 1 point per level penalty to the skill roll to injure the attacker. Can be combined with Aggressive Parry (Armed) to make for a really tough job of cutting up monster limbs and martial artist's fists and feet.
Notes: This one is okay, but it charges a point premium to unarmed attackers, still requires a roll (now with a variable penalty), and if you apply it broadly enough it because more of a genre rule than a character option.
Anything else? Sure. One option you hear sometimes is extra DR for martial artists on their arms and hands, but I find with guys doing 3d-4d damage, you can't afford enough DR to really help and make it safe. Plus, once you start armoring up your hands, your arms, your legs, and your feet, well, why not torso and head armor? I find that leads to "I may as well wear full armor." Natural point-bought DR is possible, but again, you need a lot to really matter, again, so it's charging a surcharge to guys who use a difficult attack style instead of a more powerful, longer-reaching weapon. So I find I prefer to rule it safe, and make it fit the genre.
What do I do?
I personally use the second and third of those rules - half damage parries and My Hands Are Lethal Weapons. This works pretty well. The unarmed brawler types and normally armed fighters suffer badly (but not terribly) if they fight armed opponents. But martial artists and monsters are still scary threats, and you can ward them off with your swords and axes but not get a free pass to avoid their defenses.
It's been a lot of fun. So I hope some of those suggestions work for others.